N64 games often refuse to work after accumulating even the tiniest bit of dust, which is especially likely after a period of storage. Clean the contacts of the games that don't work by first removing any dust & dirt with an air compressor, and then cleaning the metal contacts with some Isopropyl alcohol (as close to 100% Isopropyl as you can get.)
iFixit has a replacement guide for the sleep/wake button, which involves replacing the headphone jack assembly. Unfortunately iFixit doesn't sell the assembly itself, but you can source the replacement part from elsewhere on the Internet or from repair stores. iPod Nano 6th Generation Headphone Jack Assembly Replacement
There are a few different formats of memory one can use, and not all of them work with both OSX and Windows. Try this list to see which formats will work with OSX and which will not. You may need to copy your files onto a PC, reformat the drive into a format that is compatible with both OSX and Windows, and copy them back to use with your Mac.
Is the setting for "manually manage music" ticked? It should be on the "Summary" page under Devices in the left sidebar. You might need to unselect the manually manage option, or alternatively drag-and-drop your music onto your iPod.
Often when the power button dies, it's because of the ribbon connecting the button as opposed to the physical button itself. Replacing the Headphone Jack Assembly should fix your problem. You can get very cheap ribbons from places like eBay which I've had no problem with in the past, but iFixit tends to be the most reliable.
If you follow a guide such as Installing iPhone 4S Display Assembly in reverse, you will be able to identify and measure the screws as you put the phone back together. Use a small ruler to accurately measure the length of the screws.
I know this sounds ridiculous, but try turning it off and back on. If that doesn't help at all, try resetting the phone manually: hold the home and lock buttons together for ten seconds until the Apple logo shows.